The former Godfather’s Pizza CEO came under fire minutes into the debate with Rep. Michele Bachmann of Minnesota warning that under a liberal Congress and liberal president, Mr. Cain’s proposed 9 percent sales tax could jump to 90 percent. “Any time you give the Congress a brand-new tax, it doesn’t go away,” she said.

“It’s not going to fly,” he said, adding that voters in states such as New Hampshire, where there is no sales tax, have no appetite for a federal sales tax.

Former Sen. Rick Santorum of Pennsylvania cited a new analysis, released earlier in the day by the independent Tax Policy Center, that found taxes would go up for 84 percent of the nation’s households under 9-9-9.

Mr. Cain stayed relatively poised, countering that the criticisms were “knee-jerk reactions” and that his rivals were comparing apples — state sales taxes — with oranges — his proposal for a new 9 percent national sales tax on new goods.

“The reason that our plan is being attacked so much is because lobbyists, accountants, politicians, they don’t want to throw out the current tax code and put in something that’s simple and fair,” he said, responding to the barrage. “They want to continue to be able to manipulate the American people with a 10-million-word mess. Let’s throw out the 10-million-word mess and put in our plan, which will liberate the American workers and liberate American businesses.”

Mr. Romney pounced on Mr. Cain’s characterization, saying, “I am going to be getting a bushel basket that has apples and oranges in it, because I’m going to pay both taxes.”

The field then quickly turned its attention to Mr. Romney’s vow to repeal the president’s health care law, with Mr. Santorum saying that Mr. Romney doesn’t have “credibility” on the issue because “your plan was the basis for ‘Obamacare.’”

“There’s a lot of big government behind ‘Romneycare’ — not as much as ‘Obamacare,’ but a heck of a lot more than your campaign is admitting,” Newt Gingrich said, although the former House Speaker admitted that he supported an individual mandate in the past.

The event at times appeared to devolve into a rhetorical food fight, with the candidates shouting over one another in an attempt to paint the other in a poor light.

“Are you just going to keep talking?” an exasperated Mr. Romney said at one point to the energized Texas governor, who seemed clearly more combative than in previous debates. “You have a problem with allowing someone to finish speaking. I would suggest, if you want to become president of the United States, you have to let people finish speaking.”

The remarks came after Mr. Perry rehashed old allegations that surfaced in the 2008 presidential campaign that Mr. Romney hired illegal immigrants to work at his home.

“The idea that you stand here before us and talk about that you’re strong on immigration is, on its face, the height of hypocrisy,” Mr. Perry said.

In response, Mr. Romney acknowledged that he hired a lawn company that had illegal immigrants working on the crew and “when that was pointed out to us, we let them go.”

Then he tried to turn the table on Mr. Perry, highlighting his support of in-state tuition for some children of illegal immigrants and a controversial report from the Center for Immigration Studies that suggested 40 percent of all the new jobs created in Texas went to illegal immigrants — a charge Mr. Perry called “a falsehood on its face.”

At one point, Mr. Romney put his hand on Mr. Perry’s shoulder, saying: “It’s been a tough couple of debates for Rick. And I understand that so you’re going to get testy.”

Topics in the fifth debate in six weeks ranged from questions about the candidates’ personal faith and the Wall Street bailout to the Occupy Wall Street protests and the call to build a border fence.

Mr. Paul questioned how candidates who support a border fence, including Mr. Cain, Mrs. Bachmann and Mr. Romney, would pay for it. Mr. Paul later suggested that the nation could free up money to bolster the southern border by ending assistance to foreign countries and bring the troops home from overseas.

Mr. Cain found himself backtracking on two other issues during the two-hour debate.

He backed away from earlier comments about building a lethal electric fence on the Mexico border and also said he wouldn’t be willing to negotiate with terrorists, even though he suggested earlier in the day that he would be open to such a decision.

With all the fire trained on one another, the Republicans’ big target, President Obama, was left relatively unscathed.

Mr. Gingrich tried to steer the conversation back to the incumbent and voiced concerns that the intraparty squabbling will hurt the GOP’s nominee in the long run.

“Let me just point out a second that maximizing bickering is probably not the road to the White House,” Mr. Gingrich said.

Former Utah Gov. Jon Huntsman skipped the debate, part of the CNN/Western Republican Leadership Conference, in protest of the Nevada GOP’s decision to move its caucus date up to Jan. 14. That move has threatened to upend the rest of the primary schedule, with New Hampshire’s secretary of state warning he might push the first-in-the-nation primary to early December.

Last week, several of the candidates, including Mr. Gingrich and Mr. Cain, said they will join Mr. Huntsman and boycott Nevada’s caucus if the state party refuses to push it back three days, as requested by New Hampshire.

Some see the boycott effort as an attempt by cash-strapped candidates to devalue Nevada’s contest in the face of strong support here for Mr. Romney, though an uproar from some elected leaders in the Granite State and editorial in the influential New Hampshire Union Leader could turn up the political heat on the Romney camp.